Beyond deficit models of learning mathematics : Socio-cultural directions for change and research

Major paradigmatic changes in mathematics education research are drawing attention to new perspectives on learning. Whereas deficit models were previously in the foreground of research designs, these have been replaced by a wide variety of theoretical directions for studying diverse approaches to learning mathematics. There is now an acceptance of the need for richness and variety in research practices so that approaches can be studied, compared and mutually applied and improved. Psychological and quantitative approaches and methods are now increasingly complemented, or even replaced, by new directions that rely on social and anthropological theories and methods. Rather than reviving ideas about deficit research in mathematics education, the aim of this chapter is to present some socio-cultural perspectives of mathematics learning, and to show how these perspectives go beyond the deficit model of learning. Framing the main traditional markers of discrimination in school mathematics—gender, social class and ethnicity—in a perspective of social justice, the chapter concludes with a reflection on equality in terms of the democratic principle of meritocracy in mathematics education.

Subject matters of science, technology, mathematics and engineering

This chapter offers a critical review of curriculum in the STEM disciplines, overviewing contemporary context and issues around the STEM acronym as a contested space, issues of inquiry, social justice, current concerns with student engagement and their history, theoretical perspectives on teaching and learning in these disciplines, and key forms and foci of inquiry into STEM curriculum.

The age of STEM : educational policy and practice across the world in science, technology, engineering and mathematics

 Across the world STEM (learning and work in Science, Technology, Engineering and Mathematics) has taken central importance in education and the economy in a way that few other disciplines have. STEM competence has become seen as key to higher productivity, technological adaptation and research-based innovation. No area of educational provision has a greater current importance than the STEM disciplines yet there is a surprising dearth of comprehensive and world-wide information about STEM policy, participation, programs and practice.

Teaching and learning mathematics and science in a second or third language

 This study investigates the interaction between languages used for particular purposes in mathematics and science classrooms and the accompanying multimodal resources that support teachers’ strategies. The dual investigation sets this study apart, and produces its originality and contribution to the field. It develops a novel multimodal description of pedagogic strategies in multilingual mathematics and science classrooms in Malaysia.

Mid- to late Holocene landscape change and anthropogenic transformations on Mo‘orea, Society Islands: a multi-proxy approach

Archaeology’s ability to generate long-term datasets of natural and human landscape change positions the discipline as an inter-disciplinary bridge between the social and natural sciences. Using a multi-proxy approach combining archaeological data with palaeoenvironmental indicators embedded in coastal sediments, we outline millennial timescales of lowland landscape evolution in the Society Islands. Geomorphic and cultural histories for four coastal zones on Mo‘orea are reconstructed based on stratigraphic records, sedimentology, pollen analysis, and radiocarbon determinations from mid- to late Holocene contexts. Prehuman records of the island’s flora and fauna are described utilizing landsnail, insect, and botanical data, providing a palaeo-backdrop for later anthropogenic change. Several environmental processes, including sea level change, island subsidence, and anthropogenic alterations, leading to changes in sedimentary budget have operated on Mo‘orea coastlines from c. 4600 to 200 BP. We document significant transformation of littoral and lowland zones which obscured earlier human activities and created significant changes in vegetation and other biota. Beginning as early as 440 BP (1416–1490 cal. ad), a major phase of sedimentary deposition commenced which can only be attributed to anthropogenic effects. At several sites, between 1.8 and 3.0 m of terrigenous sediments accumulated within a span of two to three centuries due to active slope erosion and deposition on the coastal flats. This phase correlates with the period of major inland expansion of Polynesian occupation and intensive agriculture on the island, indicated by the presence of charcoal throughout the sediments, including wood charcoal from several economically important tree species.

Factors influencing students' choice of mathematics at university

 This study investigated what motivated current undergraduate mathematics students to choose to study mathematics at university. It found a diverse array of factors perceived by students as having informed their decisions. These included background factors, situational factors, self-perception, and perceptions of mathematics as a discipline

Studying mathematics teacher education: analysing the process of task variation on learning

Self-study of variations to task design offers a way of analysing how learning takes place. Over several years, variations were made to improve an assessment task completed by final-year teacher candidates in a primary mathematics teacher education subject. This article describes how alterations to a task informed on-going developments in self-study of one assessment task employed in an online subject. Analysis of my journal, notes from conversations with colleagues, teacher candidates’ work on the task and responses to online forums, and survey data inspired variations focused on better exploration of key concepts involved in the task, raising of focal awareness, developing a stronger professional eye in the students and the author, adaptations for multiple curriculum levels, and explorations of dual teacher–student perspectives. The overall challenge has been to support teacher candidates to learn to design effective open-ended tasks with a critical professional eye. Descriptions of the changes made to the task and the development of my own professional eye as a consequence of the application of self-study are included. Data show that variations to the task increased teacher candidates’ understanding of mathematics problem posing and generated pedagogical insights for task design.

Effect of cooling rate on phase transformations in a high-strength low-alloy steel studied from the liquid phase

The phase transformation and precipitation in a high-strength low-alloy steel have been studied over a large range of cooling rates, and a continuous cooling transformation (CCT) diagram has been produced. These experiments are unique because the measurements were made from samples cooled directly from the melt, rather than in homogenized and re-heated billets. The purpose of this experimental design was to examine conditions pertinent to direct strip casting. At the highest cooling rates which simulate strip casting, the microstructure was fully bainitic with small regions of pearlite. At lower cooling rates, the fraction of polygonal ferrite increased and the pearlite regions became larger. The CCT diagram and the microstructural analysis showed that the precipitation of NbC is suppressed at high cooling rates, and is likely to be incomplete at intermediate cooling rates.

Science and mathematics teacher education

 This entry will consider how and why science and mathematics have been linked in teacher preparation programs in ways that influence notions of content knowledge and pedagogy.

Specifying model transformations by direct manipulation using concrete visual notations and interactive recommendations

Model transformations are a crucial part of Model-Driven Engineering (MDE) technologies but are usually hard to specify and maintain for many engineers. Most current approaches use meta-model-driven transformation specification via textual scripting languages. These are often hard to specify, understand and maintain. We present a novel approach that instead allows domain experts to discover and specify transformation correspondences using concrete visualizations of example source and target models. From these example model correspondences, complex model transformation implementations are automatically generated. We also introduce a recommender system that helps domain experts and novice users find possible correspondences between large source and target model visualization elements. Correspondences are then specified by directly interacting with suggested recommendations or drag and drop of visual notational elements of source and target visualizations. We have implemented this approach in our prototype tool-set, CONVErT, and applied it to a variety of model transformation examples. Our evaluation of this approach includes a detailed user study of our tool and a quantitative analysis of the recommender system.

Solvate ionic liquids as reaction media for electrocyclic transformations

Solvate ionic liquids (SILs) consisting of lithium bis(trifluoromethylsulfonyl)imide dissolved in tri-or tetraglyme have recently emerged as a novel class of ionic liquids. Herein, the first use of solvate ionic liquids as a replacement for molecular solvents in electrocyclization reactions is reported. The SILs promoted both Diels-Alder and [2+2] cycloaddition reactions, compared to an appropriate molecular solvent, and 5 M lithium perchlorate in diethyl ether. The Gutmann acceptor number (AN) of these solvate ionic liquids has also been determined by 31P NMR spectroscopy to be 26.5, thus being modest Lewis acids.